Computer modeling of mechanical properties of biological materials can be of importance in simulating displacement of tissues during surgery, simulating mechanisms of injury and protective devices, and detection of diseased tissues. Tumors, for example, often have different mechanical properties than normal tissues. Many applications of such modeling, including estimating displacement of brain after skull opening during surgery, require an accurate material model with accurate parameters.
Several material models have been used to estimate tissue properties, mainly viscoelasticity. More recently, poroelasticity-based models have been used. While viscoelasticity characterizes tissue as an array of springs and dashpots, poroelasticity models material based on its structural components, specifically as a porous elastic matrix, with the pores saturated with a viscous fluid. This model applies to tissue like brain parenchyma, where the saturating fluid corresponds to approximately 75% of the tissue volume, and other porous tissues that may have different fluid concentrations. The elastic matrix corresponds to structural proteins such as collagen, and the fluid corresponds to cytoplasm, intracellular fluid, and blood. Poroelastic theory accounts for the fact that some of the fluid can be squeezed out of tissue when a pressure gradient is applied, and that fluid flow can damp oscillations in a manner similar to that of a hydraulic shock-absorber. Key to such models is determination of the material parameters (such as shear modulus) to accurately represent tissue.
A prior poroelastic computer algorithm for modeling mechanical properties of tissue and methods of extracting parameters, has been described by Phillip R. Perriñez, Francis E. Kennedy, Elijah E. W. Van Houten, John B. Weaver, and Keith D. Paulsen in Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography, IEEE Transactions On Biomedical Engineering, Vol. 56, No. 3, March 2009; and by Phillip R. Perriñez, Francis E. Kennedy, Elijah E. W. Van Houten, John B. Weaver, and Keith D. Paulsen in Magnetic Resonance Poroelastography: An Algorithm for Estimating the Mechanical Properties of Fluid-Saturated Soft Tissues, IEEE Transactions On Medical Imaging, Vol. 29, No. 3, March 2010. These publications show the basis of a poroelastic model and illustrate model-data mismatch when using viscoelastic models on poroelastic materials. Furthermore, the work shows that a poroelastic model provides improved numerical and spatial results over prior work using linear elastic and viscoelastic models. The system described in the attached articles requires an expensive magnetic resonance imaging system to measure motion and estimate the model parameters using magnetic resonance elastography (MRE). MRE results for mechanical properties shown in literature for a single tissue range over orders of magnitude. While some variation is expected since tissue is frequency dependent, different model-based reconstructions provide varying estimates due to differing assumptions or model-data mismatch. Therefore, it is important to validate these results with an independent mechanical test, like dynamic mechanical analyzers (DMAs).
Typical DMAs determine viscoelastic model parameters, specifically storage and loss modulus. DMA results are based on the relationship between stress (σ) and strain (ε), which are defined as σ=σ0 sin(ωt+δ) and ε=ε0 sin(ωt+δ), respectively, where ωis frequency, δ is the phase lag between the two waves, and σ0 and ε0 represent the maximum stress and strain. The storage (stored energy) and loss modulus (dissipated energy) can then be estimated as E′=σ0/ε0 (cos δ) and E″=σ0/ε0 (sin δ), respectively. A damping ratio is given as tan(δ)=E″/E′. In viscoelastic theory, the damping forces are modeled by dashpots, where the force is proportional to the velocity, illustrating the frequency dependence of the damping properties. Conversely, in poroelastic theory it is known that due to the biphasic environment, the interaction between the solid and fluid phases causes much of the attenuation. Standard DMAs use different clamps (i.e. compression, 3-point bending) to test different materials. The compression clamp typically has smooth platens that allow the material to slip transversely. Currently, empirical correction factors are used to attempt to correct errors due to this slippage.